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perlin
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/* | |
* A speed-improved perlin and simplex noise algorithms for 2D. | |
* | |
* Based on example code by Stefan Gustavson (stegu@itn.liu.se). | |
* Optimisations by Peter Eastman (peastman@drizzle.stanford.edu). | |
* Better rank ordering method by Stefan Gustavson in 2012. | |
* Converted to Javascript by Joseph Gentle. | |
* | |
* Version 2012-03-09 | |
* | |
* This code was placed in the public domain by its original author, | |
* Stefan Gustavson. You may use it as you see fit, but | |
* attribution is appreciated. | |
* | |
*/ | |
(function(global){ | |
var module = global.noise = {}; | |
function Grad(x, y, z) { | |
this.x = x; this.y = y; this.z = z; | |
} | |
Grad.prototype.dot2 = function(x, y) { | |
return this.x*x + this.y*y; | |
}; | |
Grad.prototype.dot3 = function(x, y, z) { | |
return this.x*x + this.y*y + this.z*z; | |
}; | |
var grad3 = [new Grad(1,1,0),new Grad(-1,1,0),new Grad(1,-1,0),new Grad(-1,-1,0), | |
new Grad(1,0,1),new Grad(-1,0,1),new Grad(1,0,-1),new Grad(-1,0,-1), | |
new Grad(0,1,1),new Grad(0,-1,1),new Grad(0,1,-1),new Grad(0,-1,-1)]; | |
var p = [151,160,137,91,90,15, | |
131,13,201,95,96,53,194,233,7,225,140,36,103,30,69,142,8,99,37,240,21,10,23, | |
190, 6,148,247,120,234,75,0,26,197,62,94,252,219,203,117,35,11,32,57,177,33, | |
88,237,149,56,87,174,20,125,136,171,168, 68,175,74,165,71,134,139,48,27,166, | |
77,146,158,231,83,111,229,122,60,211,133,230,220,105,92,41,55,46,245,40,244, | |
102,143,54, 65,25,63,161, 1,216,80,73,209,76,132,187,208, 89,18,169,200,196, | |
135,130,116,188,159,86,164,100,109,198,173,186, 3,64,52,217,226,250,124,123, | |
5,202,38,147,118,126,255,82,85,212,207,206,59,227,47,16,58,17,182,189,28,42, | |
223,183,170,213,119,248,152, 2,44,154,163, 70,221,153,101,155,167, 43,172,9, | |
129,22,39,253, 19,98,108,110,79,113,224,232,178,185, 112,104,218,246,97,228, | |
251,34,242,193,238,210,144,12,191,179,162,241, 81,51,145,235,249,14,239,107, | |
49,192,214, 31,181,199,106,157,184, 84,204,176,115,121,50,45,127, 4,150,254, | |
138,236,205,93,222,114,67,29,24,72,243,141,128,195,78,66,215,61,156,180]; | |
// To remove the need for index wrapping, double the permutation table length | |
var perm = new Array(512); | |
var gradP = new Array(512); | |
// This isn't a very good seeding function, but it works ok. It supports 2^16 | |
// different seed values. Write something better if you need more seeds. | |
module.seed = function(seed) { | |
if(seed > 0 && seed < 1) { | |
// Scale the seed out | |
seed *= 65536; | |
} | |
seed = Math.floor(seed); | |
if(seed < 256) { | |
seed |= seed << 8; | |
} | |
for(var i = 0; i < 256; i++) { | |
var v; | |
if (i & 1) { | |
v = p[i] ^ (seed & 255); | |
} else { | |
v = p[i] ^ ((seed>>8) & 255); | |
} | |
perm[i] = perm[i + 256] = v; | |
gradP[i] = gradP[i + 256] = grad3[v % 12]; | |
} | |
}; | |
module.seed(0); | |
/* | |
for(var i=0; i<256; i++) { | |
perm[i] = perm[i + 256] = p[i]; | |
gradP[i] = gradP[i + 256] = grad3[perm[i] % 12]; | |
}*/ | |
// Skewing and unskewing factors for 2, 3, and 4 dimensions | |
var F2 = 0.5*(Math.sqrt(3)-1); | |
var G2 = (3-Math.sqrt(3))/6; | |
var F3 = 1/3; | |
var G3 = 1/6; | |
// 2D simplex noise | |
module.simplex2 = function(xin, yin) { | |
var n0, n1, n2; // Noise contributions from the three corners | |
// Skew the input space to determine which simplex cell we're in | |
var s = (xin+yin)*F2; // Hairy factor for 2D | |
var i = Math.floor(xin+s); | |
var j = Math.floor(yin+s); | |
var t = (i+j)*G2; | |
var x0 = xin-i+t; // The x,y distances from the cell origin, unskewed. | |
var y0 = yin-j+t; | |
// For the 2D case, the simplex shape is an equilateral triangle. | |
// Determine which simplex we are in. | |
var i1, j1; // Offsets for second (middle) corner of simplex in (i,j) coords | |
if(x0>y0) { // lower triangle, XY order: (0,0)->(1,0)->(1,1) | |
i1=1; j1=0; | |
} else { // upper triangle, YX order: (0,0)->(0,1)->(1,1) | |
i1=0; j1=1; | |
} | |
// A step of (1,0) in (i,j) means a step of (1-c,-c) in (x,y), and | |
// a step of (0,1) in (i,j) means a step of (-c,1-c) in (x,y), where | |
// c = (3-sqrt(3))/6 | |
var x1 = x0 - i1 + G2; // Offsets for middle corner in (x,y) unskewed coords | |
var y1 = y0 - j1 + G2; | |
var x2 = x0 - 1 + 2 * G2; // Offsets for last corner in (x,y) unskewed coords | |
var y2 = y0 - 1 + 2 * G2; | |
// Work out the hashed gradient indices of the three simplex corners | |
i &= 255; | |
j &= 255; | |
var gi0 = gradP[i+perm[j]]; | |
var gi1 = gradP[i+i1+perm[j+j1]]; | |
var gi2 = gradP[i+1+perm[j+1]]; | |
// Calculate the contribution from the three corners | |
var t0 = 0.5 - x0*x0-y0*y0; | |
if(t0<0) { | |
n0 = 0; | |
} else { | |
t0 *= t0; | |
n0 = t0 * t0 * gi0.dot2(x0, y0); // (x,y) of grad3 used for 2D gradient | |
} | |
var t1 = 0.5 - x1*x1-y1*y1; | |
if(t1<0) { | |
n1 = 0; | |
} else { | |
t1 *= t1; | |
n1 = t1 * t1 * gi1.dot2(x1, y1); | |
} | |
var t2 = 0.5 - x2*x2-y2*y2; | |
if(t2<0) { | |
n2 = 0; | |
} else { | |
t2 *= t2; | |
n2 = t2 * t2 * gi2.dot2(x2, y2); | |
} | |
// Add contributions from each corner to get the final noise value. | |
// The result is scaled to return values in the interval [-1,1]. | |
return 70 * (n0 + n1 + n2); | |
}; | |
// 3D simplex noise | |
module.simplex3 = function(xin, yin, zin) { | |
var n0, n1, n2, n3; // Noise contributions from the four corners | |
// Skew the input space to determine which simplex cell we're in | |
var s = (xin+yin+zin)*F3; // Hairy factor for 2D | |
var i = Math.floor(xin+s); | |
var j = Math.floor(yin+s); | |
var k = Math.floor(zin+s); | |
var t = (i+j+k)*G3; | |
var x0 = xin-i+t; // The x,y distances from the cell origin, unskewed. | |
var y0 = yin-j+t; | |
var z0 = zin-k+t; | |
// For the 3D case, the simplex shape is a slightly irregular tetrahedron. | |
// Determine which simplex we are in. | |
var i1, j1, k1; // Offsets for second corner of simplex in (i,j,k) coords | |
var i2, j2, k2; // Offsets for third corner of simplex in (i,j,k) coords | |
if(x0 >= y0) { | |
if(y0 >= z0) { i1=1; j1=0; k1=0; i2=1; j2=1; k2=0; } | |
else if(x0 >= z0) { i1=1; j1=0; k1=0; i2=1; j2=0; k2=1; } | |
else { i1=0; j1=0; k1=1; i2=1; j2=0; k2=1; } | |
} else { | |
if(y0 < z0) { i1=0; j1=0; k1=1; i2=0; j2=1; k2=1; } | |
else if(x0 < z0) { i1=0; j1=1; k1=0; i2=0; j2=1; k2=1; } | |
else { i1=0; j1=1; k1=0; i2=1; j2=1; k2=0; } | |
} | |
// A step of (1,0,0) in (i,j,k) means a step of (1-c,-c,-c) in (x,y,z), | |
// a step of (0,1,0) in (i,j,k) means a step of (-c,1-c,-c) in (x,y,z), and | |
// a step of (0,0,1) in (i,j,k) means a step of (-c,-c,1-c) in (x,y,z), where | |
// c = 1/6. | |
var x1 = x0 - i1 + G3; // Offsets for second corner | |
var y1 = y0 - j1 + G3; | |
var z1 = z0 - k1 + G3; | |
var x2 = x0 - i2 + 2 * G3; // Offsets for third corner | |
var y2 = y0 - j2 + 2 * G3; | |
var z2 = z0 - k2 + 2 * G3; | |
var x3 = x0 - 1 + 3 * G3; // Offsets for fourth corner | |
var y3 = y0 - 1 + 3 * G3; | |
var z3 = z0 - 1 + 3 * G3; | |
// Work out the hashed gradient indices of the four simplex corners | |
i &= 255; | |
j &= 255; | |
k &= 255; | |
var gi0 = gradP[i+ perm[j+ perm[k ]]]; | |
var gi1 = gradP[i+i1+perm[j+j1+perm[k+k1]]]; | |
var gi2 = gradP[i+i2+perm[j+j2+perm[k+k2]]]; | |
var gi3 = gradP[i+ 1+perm[j+ 1+perm[k+ 1]]]; | |
// Calculate the contribution from the four corners | |
var t0 = 0.6 - x0*x0 - y0*y0 - z0*z0; | |
if(t0<0) { | |
n0 = 0; | |
} else { | |
t0 *= t0; | |
n0 = t0 * t0 * gi0.dot3(x0, y0, z0); // (x,y) of grad3 used for 2D gradient | |
} | |
var t1 = 0.6 - x1*x1 - y1*y1 - z1*z1; | |
if(t1<0) { | |
n1 = 0; | |
} else { | |
t1 *= t1; | |
n1 = t1 * t1 * gi1.dot3(x1, y1, z1); | |
} | |
var t2 = 0.6 - x2*x2 - y2*y2 - z2*z2; | |
if(t2<0) { | |
n2 = 0; | |
} else { | |
t2 *= t2; | |
n2 = t2 * t2 * gi2.dot3(x2, y2, z2); | |
} | |
var t3 = 0.6 - x3*x3 - y3*y3 - z3*z3; | |
if(t3<0) { | |
n3 = 0; | |
} else { | |
t3 *= t3; | |
n3 = t3 * t3 * gi3.dot3(x3, y3, z3); | |
} | |
// Add contributions from each corner to get the final noise value. | |
// The result is scaled to return values in the interval [-1,1]. | |
return 32 * (n0 + n1 + n2 + n3); | |
}; | |
// ##### Perlin noise stuff | |
function fade(t) { | |
return t*t*t*(t*(t*6-15)+10); | |
} | |
function lerp(a, b, t) { | |
return (1-t)*a + t*b; | |
} | |
// 2D Perlin Noise | |
module.perlin2 = function(x, y) { | |
// Find unit grid cell containing point | |
var X = Math.floor(x), Y = Math.floor(y); | |
// Get relative xy coordinates of point within that cell | |
x = x - X; y = y - Y; | |
// Wrap the integer cells at 255 (smaller integer period can be introduced here) | |
X = X & 255; Y = Y & 255; | |
// Calculate noise contributions from each of the four corners | |
var n00 = gradP[X+perm[Y]].dot2(x, y); | |
var n01 = gradP[X+perm[Y+1]].dot2(x, y-1); | |
var n10 = gradP[X+1+perm[Y]].dot2(x-1, y); | |
var n11 = gradP[X+1+perm[Y+1]].dot2(x-1, y-1); | |
// Compute the fade curve value for x | |
var u = fade(x); | |
// Interpolate the four results | |
return lerp( | |
lerp(n00, n10, u), | |
lerp(n01, n11, u), | |
fade(y)); | |
}; | |
// 3D Perlin Noise | |
module.perlin3 = function(x, y, z) { | |
// Find unit grid cell containing point | |
var X = Math.floor(x), Y = Math.floor(y), Z = Math.floor(z); | |
// Get relative xyz coordinates of point within that cell | |
x = x - X; y = y - Y; z = z - Z; | |
// Wrap the integer cells at 255 (smaller integer period can be introduced here) | |
X = X & 255; Y = Y & 255; Z = Z & 255; | |
// Calculate noise contributions from each of the eight corners | |
var n000 = gradP[X+ perm[Y+ perm[Z ]]].dot3(x, y, z); | |
var n001 = gradP[X+ perm[Y+ perm[Z+1]]].dot3(x, y, z-1); | |
var n010 = gradP[X+ perm[Y+1+perm[Z ]]].dot3(x, y-1, z); | |
var n011 = gradP[X+ perm[Y+1+perm[Z+1]]].dot3(x, y-1, z-1); | |
var n100 = gradP[X+1+perm[Y+ perm[Z ]]].dot3(x-1, y, z); | |
var n101 = gradP[X+1+perm[Y+ perm[Z+1]]].dot3(x-1, y, z-1); | |
var n110 = gradP[X+1+perm[Y+1+perm[Z ]]].dot3(x-1, y-1, z); | |
var n111 = gradP[X+1+perm[Y+1+perm[Z+1]]].dot3(x-1, y-1, z-1); | |
// Compute the fade curve value for x, y, z | |
var u = fade(x); | |
var v = fade(y); | |
var w = fade(z); | |
// Interpolate | |
return lerp( | |
lerp( | |
lerp(n000, n100, u), | |
lerp(n001, n101, u), w), | |
lerp( | |
lerp(n010, n110, u), | |
lerp(n011, n111, u), w), | |
v); | |
}; | |
})(this); |
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